Simplify the following expression and state the condition under which the simplification is valid: $n = \dfrac{q^2 - 5q}{q^2 - 11q + 30}$
Answer: First factor the expressions in the numerator and denominator. $ \dfrac{q^2 - 5q}{q^2 - 11q + 30} = \dfrac{(q)(q - 5)}{(q - 6)(q - 5)} $ Notice that the term $(q - 5)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(q - 5)$ gives: $n = \dfrac{q}{q - 6}$ Since we divided by $(q - 5)$, $q \neq 5$. $n = \dfrac{q}{q - 6}; \space q \neq 5$